Many free shear layers can be found in rotating systems, like atmosphere motion,oceanic currents, core dynamics or gaseous planets.We study the shear layer produced by differential rotation in cylindrical or spherical shells,numerically and experimentally.
The quasi-geostrophic model we developped is not linited to small-slope containers,accounts for global mass conservation, and fully includes the Ekman pumping effects.It has been developped to simulate as well as possible our experiments in spherical shells,involving water, sodium or galium; thermal convection or mechanical forcing; magnetic field or not.
When the depth is constant, the destabilization follows a local Reynolds number criteria, and iswell understood. However, when the depth is not constant, the instability has to break theProudman-Taylor constraint, and thus the slope plays a major role in determining the threshold.Furthermore we show that in the latter case, the instability is a Rossby wave.
A first experiment consists of two corotating disks in a spherical shell, which drive a shearlayer. We study the stability threshold, and the instabilities that take place. We obtain asymptotical laws, supported by simple theoretical considerations, as well as numerical results.A second experiment uses an ″inner core″ that is differentially rotating to generate the shear layer.Again, the stability threshold is studied and asymptotical laws are exhibited.
Recently, we found that such quasi-geostrophic flows are able to produce magnetic fields.Taking advantage of the quasi-geostrophic nature of the flow, we are writing a numerical codethat could be able to lower both Ekman and Prandtl number significantly compared toregular geodynamo simulations. |
|
|